My [32M] father [65M] completely disconnected himself from our family since the birth of my child

My relationship with my father has always been distant at best. When I was living with him he was always extremely strict and we would not talk much at all. He's never agreed with my lifestyle choices and it's always felt I've never met his expecations he set for me. He immigrated here in his 20's and raised me and my two sisters with my mother in California. He worked hard, long hours, saved a lot and was very conservative with money. I moved out at 22 and lived a more "millennial" life. I've been able to hold down good and stable job my whole life, but never saved much money (at least by his standards). I traveled and spent a lot.
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Fast forward to now.. I am 32 and have a 4 month old with my girlfriend of 5 years. While my father has been distant in the past hes completely cut us off since he heard about the pregnancy. He used to at least show up to family gatherings and events but now he just doesnt go. He has not seen us during the whole pregnancy and after up until now. It makes things extremely awkward for our family
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My main concern is that it is putting enormous stress on my mother who still lives with him as she wants to be part of her granddaughters life. My mother is unable to visit us on her own as our father does all the driving. We don't bring the baby to their house. In the mean time I've been making the 3 hour double round trip to bring my mom to our house and bring her back and its tiring me out. I don't hear too much about it but they are definitely fighting a lot in their own house as well.
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When I try to talk to my father about it feels like he still thinks of me as an irresponsible child. He wants to know and control our spending and finances. He's asked for a paternity test to prove its my child. He doesn't trust me or my girlfriend at all to take care of ourselves and a child.
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I've always thought it would get better with time... moving out and showing him that I am doing ok but it has clearly gotten worse. Me and my sisters believe he has a fear of us moving back in and asking for handouts. We have all moved out for more than 5 years now, myself for more than 10 without asking for anything... not sure what more I can do. How can I fix our family?

--- **TL;DR;** : father has completely cut himself off from our family since the birth of my child. its stressing out our family and especially my mother. what can we do to fix this?

Source.